Diagram groups and directed 2-complexes: homotopy and homology.

DOI10.1016/j.jpaa.2005.06.012zbMath1163.20027arXivmath/0301225OpenAlexW2093120826MaRDI QIDQ814771

Victor S. Guba, Mark V. Sapir

Publication date: 7 February 2006

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301225

zbMATH Keywords

presentationsPoincaré seriesfundamental groupsfinitely presented groupsdirected graphsThompson group \(F\)homotopy groupsdiagram groupsstring rewriting systemsdirected \(2\)-complexesinteger homology groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Topological methods in group theory (57M07) Homological methods in group theory (20J05) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items

A Lyndon's identity theorem for one-relator monoids, Hyperplanes of Squier's cube complexes, On diagram groups over Fibonacci-like semigroup presentations and their generalizations, On Jones' subgroup of R. Thompson group \(F\), R. Thompson’s group and the amenability problem, On the dimension growth of groups., Topological finiteness properties of monoids. I: Foundations, Congruence subgroups and crystallographic quotients of small Coxeter groups, The Generation Problem in Thompson Group 𝐹, On subgroups of R. Thompson’s group $F$, SURFACE SUBGROUPS OF RIGHT-ANGLED ARTIN GROUPS, Growth of positive words and lower bounds of the growth rate for Thompson’s groups F(p), SOME GROUP THEORY PROBLEMS, Hyperbolic diagram groups are free, Finiteness properties of cubulated groups, Universal diagram groups with identical Poincaré series., On properties not inherited by monoids from their Schützenberger groups., Actions of picture groups on CAT(0) cubical complexes., Homological and finiteness properties of picture groups, On the conjugacy growth functions of groups., Groupoids and the algebra of rewriting in group presentations, A strong geometric hyperbolicity property for directed graphs and monoids., QUASI-ISOMETRY AND FINITE PRESENTATIONS OF LEFT CANCELLATIVE MONOIDS, Diagram groups and directed 2-complexes: homotopy and homology., Diagram groups are totally orderable.

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